Philippe Tranchida

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20242026

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math.GR2026

The geometry of wreath and semi-direct products

Claudio Alexandre Piedade, Philippe Tranchida

Coset geometries are incidence geometries constructed from a group $G$ and a system of subgroups $(G_{i})_{i \in I}$ of subgroups of $G$ . For any algebraic group operation, it is the…

math.GR2025

Groups represented by incidence geometries

Dimitri Leemans, Klara Stokes, Philippe Tranchida

The aim of this paper is to use the framework of incidence geometry to develop a theory that permits to model both the inner and outer automorphisms of a group G simultaneously. Mo…

math.GR2025

From Group Operations to Geometric Structures: Amalgamations, HNN-Extensions, and Twisting in Coset Geometries

Claudio Alexandre Piedade, Philippe Tranchida

Coset incidence geometries, introduced by Jacques Tits, provide a versatile framework for studying the interplay between group theory and geometry. In this article, we build upon t…

math.GR2024

Triples of involutions in PGL(2,q) and their incidence geometries

Philippe Tranchida

For $q = p^{n}$ with $p$ an odd prime, the projective linear group $P G L (2, q)$ can be seen as the stabilizer of a conic $O$ in a projective plane $I ¨ = P G (2, q)$ . In that setting, invol…